The　study　of　quaternionic　Gabor　systems　has　interested　some　mathematicians　in　recent　years.　From　the　literature,　we　found　that　most　existing　results　on　quaternionic　Gabor　frames　focus　on　the　case　of　the　product　of　time-frequency　shift　parameters　being　equal　to　1,　and　have　a　gap　that　the　involved　quaternionic　Gabor　systems　are　all　incomplete　according　to　the　symmetric　real　scalar　inner　product.　In　this　paper,　we　introduce　quaternionic　Zak　transformation　and　a　class　of　quaternionic　Gabor　systems.　Under　the　condition　that　the　products　of　time-frequency　shift　parameters　are　rational　numbers,　we　characterize　completeness　and　frame　property　of　quaternionic　Gabor　systems　in　terms　of　Zak　transformation　matrices.　From　this,　we　derive　the　density　theorem　for　quaternionic　Gabor　systems.